A Pexider difference associated to a Pexider quartic functional equation in topological vector spaces

On Pexider Differences in Topological Vector Spaces

and Applied Analysis 3 It follows from 2.1 and 2.6 that 2f ( x y 2 ) − g x − h(y) 2f ( x y 2 ) − g(y z) − h x − z − [ 2f (x z 2 ) − g 2z − h x − z ] [ 2f ( y 2z 2 ) − g 2z − h(y) ] − [ 2f ( y 2z 2 ) − g(y z) − h z ] [ 2f (x z 2 ) − g x − h z ] ∈ 3V − 2V 2.7 for all x, y ∈ X with ‖x‖ ‖y‖ < d. Hence, by 2.1 and 2.7 , we have 2f ( x y 2 ) − g x − h(y) ∈ 3V − 2V 2.8 for all x, y ∈ X. Letting x 0 y ...

Superstability of Some Pexider-Type Functional Equation

Hyers–ulam–rassias Stability of a Generalized Pexider Functional Equation

In this paper, we obtain the Hyers–Ulam–Rassias stability of the generalized Pexider functional equation ∑ k∈K f(x+ k · y) = |K|g(x) + |K|h(y), x, y ∈ G, where G is an abelian group, K is a finite abelian subgroup of the group of automorphism of G. The concept of Hyers–Ulam–Rassias stability originated from Th.M. Rassias’ Stability Theorem that appeared in his paper: On the stability of the lin...

On the Superstability of the Pexider Type Trigonometric Functional Equation

We will investigate the superstability of the hyperbolic trigonometric functional equation from the following functional equations: fx y ± gx − y λfxgy andfx y ± gx − y λgxfy, which can be considered the mixed functional equations of the sine function and cosine function, the hyperbolic sine function and hyperbolic cosine function, and the exponential functions, respectively.

The Superstability of the Pexider Type Trigonometric Functional Equation

The aim of this paper is to investigate the stability problem for the Pexider type (hyperbolic) trigonometric functional equation f(x + y) + f(x + σy) = λg(x)h(y) under the conditions : |f(x + y) + f(x + σy)− λg(x)h(y)| ≤ φ(x), φ(y), and min{φ(x), φ(y)}. As a consequence, we have generalized the results of stability for the cosine(d’Alembert), sine, and the Wilson functional equations by J. Bak...